A sharp knife has a smaller area of contact with the object to be cut.

For the same force exerted, a smaller area gives greater pressure as indicated by Pressure = Force / Area

2.

*Explain why the height of the mercury in a barometer remains unchanged when the diameter of the inverted tube is changed.

Since Pressure = (height of liquid column) x (density of liquid) x (gravitational field strength), then the height = pressure / [(density of liquid) x (gravitational field strength)]. It means that the height of the mercury in the barometer depends only on the pressure and gravitational field strength.

3.

*Explain why the atmospheric pressure decreases with height

The pressure at any given altitude in the atmosphere is due to the weight of the air above.

As altitude increases, there will be less air above. The density of air also decreases.

Since Pressure = (height of liquid column) x (density of liquid) x (gravitational field strength), a decrease in height and density of the air column (or any other fluid) will lead to a decrease in pressure.